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Intern  Joined: 19 Sep 2010
Posts: 21
Working together, John and Jack can type 20 pages in one hou  [#permalink]

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16 00:00

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(N/A)

Question Stats: 76% (02:14) correct 24% (03:03) wrong based on 511 sessions

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Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

A. 1/3
B. 2/5
C. 1/2
D. 2/3
E. 3/5
Math Expert V
Joined: 02 Sep 2009
Posts: 61537
Re: Hours to type pages  [#permalink]

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6
2
Barkatis wrote:
how would you solve this one ?

Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

1/3
2/5
1/2
2/3
3/5

Let the rate of John be $$x$$ pages per hour and the rate of Jack $$y$$ pages per hour. Then as we can sum the rates and $$rate*time=job$$: $$(x+y)*1=20$$ --> $$x+y=20$$;

"They would be able to type 22 pages in one hour if Jack increases his typing speed by 25%": $$(x+1.25y)*1=22$$ --> $$x+1.25y=22$$;

Question: $$\frac{y}{x}=?$$

Subtract (1) from (2) --> $$x+1.25y-(x+y)=22-20$$ --> $$0.25y=2$$ --> $$y=8$$ --> $$x=12$$ --> $$\frac{y}{x}=\frac{8}{12}=\frac{2}{3}$$.

OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: $$0.25y=2$$ --> --> $$y=8$$ --> $$x=12$$ --> $$\frac{y}{x}=\frac{8}{12}=\frac{2}{3}$$.

_________________
Retired Moderator Joined: 02 Sep 2010
Posts: 708
Location: London
Re: Hours to type pages  [#permalink]

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4
3
Barkatis wrote:
how would you solve this one ?

Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

1/3
2/5
1/2
2/3
3/5

Lets say John types x pages an hour and Jack types y pages an hour.

We know that x+y=20

Jack increase speed by 25% means he will type 1.25y pages an hour.

So we get x+1.25y=22

We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).

Subtracting both : 0.25y=2 so y=8 ... so x=12
(y/x)=2/3

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##### General Discussion
Intern  Joined: 19 Sep 2010
Posts: 21
Re: Hours to type pages  [#permalink]

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Here is the way I solve it using the formula RATE = JOB / TIME

Let x be the Job done by Jack in one hour and y the job done by Johon in one hour.

Working together, John and Jack can type 20 pages in one hour : x/1 + y/1 = 20/1

they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%: 5/4(x/1) + y/1 = 22/1

Thus x=8 ; y=12
x/y = 2/3
Senior Manager  S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 398
Re: Hours to type pages  [#permalink]

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Let the rate of John be x pages per hour and the rate of Jack y pages per hour.

so x + y = 20------------(i)
After 25% increase by y
x + 1.25y = 22-----------(ii)
Solving i and ii
y = 8
x = 12
Ratio = 2/3
Ans. D
_________________
Intern  Joined: 23 May 2010
Posts: 3
Re: Hours to type pages  [#permalink]

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x+y=20
4x+5y=88
x=8
y=12

==>D
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1713
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Working together, John and Jack can type 20 pages in one hou  [#permalink]

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Let the Rate of John = a & Rate of Jack = b

Let the combined time taken = t

(a+b)t = 20 ............... (1)

25% increase in rate of Jack $$= \frac{125b}{100}$$

$$(a + \frac{125b}{100})t = 22$$ ......... (2)

$$\frac{a+b}{a+1.25b} = \frac{10}{11}$$

$$\frac{b}{a} = \frac{2}{3}$$

Senior Manager  Joined: 07 Aug 2011
Posts: 492
GMAT 1: 630 Q49 V27
Working together, John and Jack can type 20 pages in one hou  [#permalink]

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1
Barkatis wrote:
Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

A. 1/3
B. 2/5
C. 1/2
D. 2/3
E. 3/5

so we are told that Jack's 25% typing speed contributes 2 pages , 100% speed would contribute 8 pages in an hours. So JACK types 8 Pages
and JOHN types 12 Pages in an hour time.

Ratio of their speed :
$$\frac{8}{12} = \frac{2}{3}$$
Manager  Joined: 18 Dec 2014
Posts: 99
Re: Working together, John and Jack can type 20 pages in one hou  [#permalink]

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Jack + John = 20 per hour
Jack increase 25% = 22 per hour
25% = 2
100% = 8
Jack 100% = 8 per hour

20 - 8 = 12 per hour

John = 12 per hour
Jack = 8 per hour

8 / 12 =
2 / 3
Senior Manager  Joined: 15 Sep 2011
Posts: 302
Location: United States
WE: Corporate Finance (Manufacturing)
Re: Working together, John and Jack can type 20 pages in one hou  [#permalink]

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Signature VeritasPrepKarishma move: If 2 is 25% of a number, the number is 8 and therefore, the new ratio is 10:12 and the old ratio 8:12 = 2:3 Non-Human User Joined: 09 Sep 2013
Posts: 14161
Re: Working together, John and Jack can type 20 pages in one hou  [#permalink]

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_________________ Re: Working together, John and Jack can type 20 pages in one hou   [#permalink] 15 Feb 2018, 22:34
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